A Test Matrix for an Inverse Eigenvalue Problem

A Test Matrix for an Inverse Eigenvalue Problem

We present a real symmetric tridiagonalmatrix of order nwhose eigenvalues are {2k}n−1 k=0 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l + 1}n−2 l=0 . Thematrix entries are explicit functions of the size n, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution ...

On an Inverse Eigenvalue Problem for Unitary

We show that a unitary upper Hessenberg matrix with positive subdiago-nal elements is uniquely determined by its eigenvalues and the eigenvalues of a modiied principal submatrix. This provides an analog of a well-known result for Jacobi matrices.

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

A Computer Aided Existence and Uniqueness Proof for an Inverse Matrix Eigenvalue Problem

On an Inverse Eigenvalue Problem for a Semilinear Sturmäliouville Operator